def fit_rabi_with_phase_on_linslope(g_f, g_A, g_a, g_b, g_phi, *arg):
"""
fits (and plots) a cosine on a slope, with offset,
y(x) = a + bx + Acos(f*x + phi)
Initial guesses (1st args, in this order):
g_f : float
guess for the frequency
g_A : float
guess for amplitude
g_a : float
guess for offset
g_b = 0. : float
guess for slope
g_phi = 0. : float
guess for the phase
"""
fitfunc_str = "a + b*x + A*cos(2pi*f*x + phi)"
f = fit.Parameter(g_f, 'frequency')
A = fit.Parameter(g_A, 'amplitude')
a = fit.Parameter(g_a, 'offset')
b = fit.Parameter(g_b, 'slope')
phi = fit.Parameter(g_phi, 'phase')
p0 = [f, A, a, b, phi]
def fitfunc(x):
return a() + b() * x + A() * cos(2 * pi * f() * x + phi())
return p0, fitfunc, fitfunc_str
def fit_rabi_simple(g_f, g_A, g_a, g_phi, *arg):
"""
fits a cosine thats damped exponentially,
y(x) = a + A * cos(2pi*f*x)
Initial guesses, in this order:
g_f : frequency
g_A : initial amplitude of the oscillation
g_a : offset
"""
fitfunc_str = "a + A * cos(f*x + phi)"
f = fit.Parameter(g_f, 'f')
A = fit.Parameter(g_A, 'A')
a = fit.Parameter(g_a, 'a')
phi = fit.Parameter(g_phi, 'phi')
# tau = fit.Parameter(g_tau, 'tau')
p0 = [f, A, a, phi]
def fitfunc(x):
return a() + A() * cos(2 * pi * (f() * x + phi() / 360.))
return p0, fitfunc, fitfunc_str
def fit_rabi_damped_exp(g_f, g_A, g_a, g_tau, *arg):
"""
fits a cosine thats damped exponentially,
y(x) = a + A * exp(-x/tau) * cos(f*x + phi)
Initial guesses, in this order:
g_f : frequency
g_A : initial amplitude of the oscillation
g_a : offset
### g_phi : phase
g_tau : decay constant
"""
fitfunc_str = "a + A * exp(-x/tau) * cos(f*x + phi)"
f = fit.Parameter(g_f, 'f')
A = fit.Parameter(g_A, 'A')
a = fit.Parameter(g_a, 'a')
phi = fit.Parameter(0., 'phi')
tau = fit.Parameter(g_tau, 'tau')
p0 = [f, A, a, tau, phi]
#print tau
def fitfunc(x):
return a() + A() * exp(-x / tau()) * cos(2 * pi *
(f() * x + phi() / 360.))
return p0, fitfunc, fitfunc_str
def fit_AOM_powerdependence(g_a, g_xc, g_k, *arg):
fitfunc_str = 'a * exp(-exp(-k*(x-xc)))'
a = fit.Parameter(g_a, 'a')
xc = fit.Parameter(g_xc, 'xc')
k = fit.Parameter(g_k, 'k')
p0 = [a, xc, k]
def fitfunc(x):
return a() * np.exp(-np.exp(-k() * (x - xc())))
return p0, fitfunc, fitfunc_str
def fit_ramsey_gaussian_decay(g_tau, g_a, *arg):
"""
fitfunction for a ramsey modulation, with gaussian decay,
y(x) = a + A*exp(-(x/tau)**2) * mod,
where:
mod = sum_i(cos(2pi*f_i*x + phi_i) - 1)
Initial guesses (in this order):
g_tau : decay const
g_A : Amplitude
g_a : offset
For the modulation:
an arbitrary no of tuples, in the form
(g_f, g_A, g_phi)[i] = (frequency, Amplitude, phase)[i]
"""
fitfunc_str = 'y(x) = a + exp(-(x/tau)**2)*('
no_frqs = len(arg)
if no_frqs == 0:
print 'no modulation frqs supplied'
return False
tau = fit.Parameter(g_tau, 'tau')
# A = fit.Parameter(g_A, 'A')
a = fit.Parameter(g_a, 'a')
p0 = [tau, a]
print 'fitting with %d modulation frequencies' % no_frqs
frqs = []
amplitudes = []
phases = []
for i, m in enumerate(arg):
fitfunc_str += 'A%d*cos(2pi*f%d*x + phi%d) + ' % (i, i, i)
frqs.append(fit.Parameter(m[0], 'f%d'%i))
phases.append(fit.Parameter(m[2], 'phi%d'%i))
amplitudes.append(fit.Parameter(m[1], 'A%d'%i))
p0.append(frqs[i])
p0.append(amplitudes[i])
p0.append(phases[i])
fitfunc_str += ')'
def fitfunc(x):
prd = exp(-(x/tau())**2)
mod = 0
for i in range(no_frqs):
mod += amplitudes[i]() * (cos(2*pi*frqs[i]()*x + phases[i]()))
return a() + prd*mod
return p0, fitfunc, fitfunc_str
def fit_cos(g_f, g_a, g_A, g_phi, *arg):
fitfunc_str = 'A * cos(2pi * (f*x + phi/360) ) + a'
f = fit.Parameter(g_f, 'f')
a = fit.Parameter(g_a, 'a')
A = fit.Parameter(g_A, 'A')
# phi = fit.Parameter(g_phi, 'phi')
p0 = [f, a, A] #, phi]
def fitfunc(x):
return a() + A() * np.cos(2 * np.pi * (f() * x + 0)) #phi()/360.))
return p0, fitfunc, fitfunc_str
def fit_gauss(g_a, g_A, g_x0, g_sigma):
fitfunc_str = 'a + A * exp(-(x-x0)**2/sigma**2)'
a = fit.Parameter(g_a, 'a')
x0 = fit.Parameter(g_x0, 'x0')
A = fit.Parameter(g_A, 'A')
sigma = fit.Parameter(g_sigma, 'sigma')
p0 = [a, x0, A, sigma]
def fitfunc(x):
return a() + A() * np.exp(-(x - x0())**2 / sigma()**2)
return p0, fitfunc, fitfunc_str
def fit_population_vs_detuning(g_a, g_A, g_F, g_x0, *arg):
fitfunc_str = 'a + A * F**2/(F**2+(x-x0)**2) * sin(pi/(2F) * sqrt(F**2+(x-x0)**2))**2'
A = fit.Parameter(g_A, 'A')
a = fit.Parameter(g_a, 'a')
F = fit.Parameter(g_F, 'F')
x0 = fit.Parameter(g_x0, 'x0')
p0 = [a, A, F, x0]
def fitfunc(x):
return a() + A() * F()**2 / (F()**2 + (x - x0())**2) * sin(
pi / F() / 2. * sqrt(F()**2 + (x - x0())**2))**2
return p0, fitfunc, fitfunc_str
def fit_rabi_multiple_detunings(g_A, g_a, g_F, g_tau, *arg):
"""
fitfunction for an oscillation that drives several transitions
(several nuclear lines, for instance)
y(x) = a + A * sum_I[ F**2/(F**2 + delta_i**2) *
(cos(sqrt(F**2 + delta_i**2 + phi_i)) - 1) * exp(-x/tau)
Initial guesses:
g_A : full Rabi amplitude
g_a : offset
g_F : Rabi frequency
g_tau : exp decay constant
For the driven levels:
all successive args are treated as detunings for additional
levels, (delta_i, g_phi_i) -- given as tuples!
detuning is not a free param, but is given exactly.
"""
fitfunc_str = "a + A * sum_I[ F**2/(F**2 + delta_i**2) * (cos(sqrt(F**2 + delta_i**2 + phi_i)) - 1) * exp(-x/tau)"
no_detunings = len(arg)
A = fit.Parameter(g_A, 'A')
a = fit.Parameter(g_a, 'a')
F = fit.Parameter(g_F, 'F')
tau = fit.Parameter(g_tau, 'tau')
p0 = [A, a, F, tau]
detunings = []
phases = []
for i, d in enumerate(arg):
fitfunc_str += '\ndetuning d%d := %f' % (i, d[0])
detunings.append(d[0])
#phases.append(fit.Parameter(d[1], 'phi%d'%i))
#p0.append(phases[i])
def fitfunc(x):
val = a()
for i, d in enumerate(detunings):
f2 = F()**2 + d**2
val += A() * (F()**2 / f2) * (cos(2 * pi * sqrt(f2) * x + 0.) - 1)
return val * exp(-x / tau())
return p0, fitfunc, fitfunc_str
def fit_FID_gauss(g_tau, g_A, g_a, *arg):
"""
fitfunction for a gaussian decay,
y(x) = a + A*exp(-(x/tau)**2)
Initial guesses (in this order):
g_tau : decay constant
g_A : amplitude
g_a : offset
"""
tau = fit.Parameter(g_tau, 'tau')
A = fit.Parameter(g_A, 'A')
a = fit.Parameter(g_a, 'a')
p0 = [tau, A, a]
def fitfunc(x): return a() + A()*exp(-(x/tau())**2)
return p0, fitfunc, fitfunc_str
def fit_saturation(g_A, g_xsat, *arg):
"""
fitfunction for a saturation (e.g., the NV PL)
y(x) = A * x / (x + xsat)
I.g.:
g_A : maximum signal (at x=infinity)
g_xsat : saturation point
"""
fitfunc_str = 'A * x / (x + x_sat)'
A = fit.Parameter(g_A, 'A')
xsat = fit.Parameter(g_xsat, 'xsat')
p0 = [A, xsat]
def fitfunc(x):
return A() * x / (x + xsat())
return p0, fitfunc, fitfunc_str
def fit_echo(g_tau, g_A, g_a, g_k, *arg):
"""
fitfunction for a gaussian decay,
y(x) = a + A*exp(-(x/tau)**k)
Initial guesses (in this order):
g_tau : decay constant
g_A : amplitude
g_a : offset
g_k : exponent
"""
fitfunc_str='a() + A()*exp(-(x/tau))**k)'
tau = fit.Parameter(g_tau, 'tau')
A = fit.Parameter(g_A, 'A')
a = fit.Parameter(g_a, 'a')
k = fit.Parameter(g_k,'k')
p0 = [tau, A, a,k]
def fitfunc(x): return a() + A()*exp(-(x/tau())**k())
return p0, fitfunc, fitfunc_str
def fit_rabi_damped_exp_on_linslope(g_f, g_A, g_a, g_b, g_phi, g_tau, *arg):
"""
fits (and plots) a cosine on a slope, with offset,
y(x) = a + bx + Acos(f*x + phi) * exp(-x/tau)
Initial guesses (1st args, in this order):
g_f : float
guess for the frequency
g_A : float
guess for amplitude
g_a : float
guess for offset
g_b : float
guess for slope
g_phi : float
guess for the phase
g_tau : float
decay constant
"""
fitfunc_str = "a + b*x + A*cos(2pi*f*x + phi) * exp(-x/tau)"
f = fit.Parameter(g_f, 'frequency')
A = fit.Parameter(g_A, 'amplitude')
a = fit.Parameter(g_a, 'offset')
b = fit.Parameter(g_b, 'slope')
phi = fit.Parameter(g_phi, 'phase')
tau = fit.Parameter(g_tau, 'tau')
p0 = [f, A, a, b, phi, tau]
def fitfunc(x):
return a() + b() * x + A() * cos(2 * pi * f() * x + phi()) * exp(
-x / tau())
return p0, fitfunc, fitfunc_str
def fit_exp_decay_with_offset(g_a, g_A, g_tau, *arg):
"""
fitfunction for an exponential decay,
y(x) = A * exp(-x/tau) + a
Initial guesses (in this order):
g_a : offset
g_A : initial Amplitude
g_tau : decay constant
"""
fitfunc_str = 'A * exp(-x/tau) + a'
a = fit.Parameter(g_a, 'a')
A = fit.Parameter(g_A, 'A')
tau = fit.Parameter(g_tau, 'tau')
p0 = [a, A, tau]
def fitfunc(x):
return a() + A() * np.exp(-x / tau())
return p0, fitfunc, fitfunc_str
def fit_poly(indices, *arg):
fitfunc_str = 'sum_n ( a[n] * x[n] )'
idx = 0
p0 = []
for i, a in enumerate(indices):
p0.append(fit.Parameter(a, 'a%d' % i))
def fitfunc(x):
val = 0
for i in range(len(indices)):
val += p0[i]() * x**i
return val
return p0, fitfunc, fitfunc_str
def fit_saturation_with_offset_linslope(g_a, g_b, g_A, g_xsat, *arg):
"""
fitfunction for a saturation (e.g., the NV PL)
y(x) = a + b*x + A * x / (x + xsat)
I.g.:
g_a : offset
g_b : linear slope
g_A : maximum signal (at x=infinity)
g_xsat : saturation point
"""
fitfunc_str = 'a + b*x + A * x / (x + x_sat)'
a = fit.Parameter(g_a, 'a')
b = fit.Parameter(g_b, 'b')
A = fit.Parameter(g_A, 'A')
xsat = fit.Parameter(g_xsat, 'xsat')
p0 = [a, b, A, xsat]
def fitfunc(x):
return a() + b() * x + A() * x / (x + xsat())
return p0, fitfunc, fitfunc_str
def fit_ESR_gauss(g_a, g_A, g_sigma, g_x0, *arg):
"""
fitfunction for gaussian esr dips,
y(x) = a - A*sum_i(exp(-((x-x0_i)/sigma)**2))
Initial guesses (in this order):
g_a : offset
g_A : dip depth (all the same)
g_sigma : std dev of the dip width (all the same)
g_x0 : zero-point of the esr pattern
For the splittings:
an arbitrary amount of splits, in the form
(m, g_s) : where m=multiplicity, g_s=initial guess for the
splitting of two neighboring dips
Example:
giving (2, 2e3), (3, 2e3), would describe two splittings,
e.g., the two-fold one for the zeeman splitting of the +/-1
manifolds, and on top of that the 3-fold splitting of the N14.
This results in 6 peaks in total, where 4 of them appear,
because of the equal splitting in the two cases, on top
of each other, yielding 2 low, and two deep dips.
"""
fitfunc_str = 'a - A*sum_i(exp(-((x-x0_i)/sigma)**2))'
no_splits = len(arg)
a = fit.Parameter(g_a, 'a')
A = fit.Parameter(g_A, 'A')
sigma = fit.Parameter(g_sigma, 'sigma')
x0 = fit.Parameter(g_x0, 'x0')
p0 = [a, A, sigma, x0]
print 'fitting with %d splittings' % no_splits
splits = []
for i, s in enumerate(arg):
fitfunc_str += '\nsplitting s%d with multiplicity %d' % (i, s[0])
splits.append(fit.Parameter(s[1], 's%d'%i))
p0.append(splits[i])
# remove the fixed params from the p0 array
# fixedp = []
# for i,p in enumerate(p0):
# if i in fixedsplits:
# fixedp.append(p)
# for p in fixedp:
# p0.remove(p)
def fitfunc(x):
pts = [x0()]
pts_next = []
# generate the points where the dips sit for the current param
# values
for i in range(no_splits):
m = arg[i][0]
s = arg[i][1]
for pt in pts:
j = 0
while j < m:
split = splits[i]()
pts_next.append(pt-split*(m-1.)/2. + j*split)
j+=1
pts = pts_next
pts_next = []
depth = 0.
for p in pts:
depth += A() * exp(-((x-p)/sigma())**2)
return a() - depth
return p0, fitfunc, fitfunc_str
#V_EOM[n_steps+1,0] = 0
#measured_power[n_steps+1,0] = powermeter.get_power()
#data.add_data_point(V_EOM[n_steps+1,0],measured_power[n_steps+1,0])
AWG.set_ch4_offset(0) #set EOM channel to back to 0 to avoid drift
AWG.set_ch4_marker1_low(0) #set AOM voltage back to zero again
data.close_file()
# the fitting procedure applies only if fit_calibration_curve is flagged above!
if fit_calibration_curve:
def num2str(num, precision):
return "%0.*f" % (precision, num)
A = fit.Parameter(max(measured_power - BG) / 2)
B = fit.Parameter(max(measured_power - BG) / 2)
f = fit.Parameter(1 / 2.5)
phi = fit.Parameter(0)
def fit_cos(x):
return A() + B() * cos(2 * pi * f() * x + phi())
ret = fit.fit1d(V_EOM.reshape(-1),
measured_power.reshape(-1) - BG,
None,
fitfunc=fit_cos,
p0=[A, B, f, phi],
do_plot=True,
do_print=True,
ret=True)